Click on the image to open a larger version. Copyright: Michael Berry
“The picture shows light from a broadened laser beam that has been shone through rippling bathroom-window glass. John Barker drew my attention to this unusual pattern in 1974. Taking the picture was a moment of sudden understanding – a ‘clariton’ – bringing several connections, fundamental in optics and more generally wave physics, including quantum theory.
I had just read René Thom’s book Stabilité Structurelle et Morphogenèse, in which he introduced his mathematical ‘catastrophe theory’ and explained that the forms he had classified correspond to optical caustics (regions of focusing – the brightest places) in the physics of light. It was immediately clear that the bright curves in the bathroom-window picture were perfect illustrations in ray optics of these geometrical singularities (in fact, the ‘fold’, ‘cusp’, and ‘hyperbolic umbilic’ singularities). Moreover, the delicate patterns that decorate the ray patterns were wave interference effects giving depth and structure to the geometrical singularities. In the glass I used (Pilkington’s ‘Pacific’), the rippling formed a regular array; this meant that on the finest scale the intensity was a series of spots, identical to the Bragg beams studied in X-ray crystallography.
These patterns inhabit the conceptual boundary between rays and waves. Previously, I had studied rudimentary versions in quantum physics (scattering of molecules, electrons diffracted by crystals, atoms reflected from crystal surfaces...). Seeing the theoetical patterns with my own eyes brought the theory to life and to completion, and stimulated the development of the new field of ‘catastrophe optics’, leading to more general understanding of how different levels of description in physics are both complicated and enriched by the presence of singularities.”
Michael Berry is is Editor of Proceedings of the Royal Society A.